Synergy of semiempirical models and machine learning in computational chemistry

Catalyzed by enormous success in the industrial sector, many research programs have been exploring data-driven, machine learning approaches. Performance can be poor when the model is extrapolated to new regions of chemical space, e.g., new bonding types, new many-body interactions. Another important limitation is the spatial locality assumption in model architecture, and this limitation cannot be overcome with larger or more diverse datasets. The outlined challenges are primarily associated with the lack of electronic structure information in surrogate models such as interatomic potentials. Given the fast development of machine learning and computational chemistry methods, we expect some limitations of surrogate models to be addressed in the near future; nevertheless spatial locality assumption will likely remain a limiting factor for their transferability. Here, we suggest focusing on an equally important effort-design of physics-informed models that leverage the domain knowledge and employ machine learning only as a corrective tool. In the context of material science, we will focus on semi-empirical quantum mechanics, using machine learning to predict corrections to the reduced-order Hamiltonian model parameters. The resulting models are broadly applicable, retain the speed of semiempirical chemistry, and frequently achieve accuracy on par with much more expensive ab initio calculations. These early results indicate that future work, in which machine learning and quantum chemistry methods are developed jointly, may provide the best of all worlds for chemistry applications that demand both high accuracy and high numerical efficiency.

NEXMD v2.0 Software Package for Nonadiabatic Excited State Molecular Dynamics Simulations

We present NEXMD version 2.0, the second release of the NEXMD (Nonadiabatic EXcited-state Molecular Dynamics) software package. Across a variety of new features, NEXMD v2.0 incorporates new implementations of two hybrid quantum-classical dynamics methods, namely, Ehrenfest dynamics (EHR) and the Ab-Initio Multiple Cloning sampling technique for Multiconfigurational Ehrenfest quantum dynamics (MCE-AIMC or simply AIMC), which are alternative options to the previously implemented trajectory surface hopping (TSH) method. To illustrate these methodologies, we outline a direct comparison of these three hybrid quantum-classical dynamics methods as implemented in the same NEXMD framework, discussing their weaknesses and strengths, using the modeled photodynamics of a polyphenylene ethylene dendrimer building block as a representative example. We also describe the expanded normal-mode analysis and constraints for both the ground and excited states, newly implemented in the NEXMD v2.0 framework, which allow for a deeper analysis of the main vibrational motions involved in vibronic dynamics. Overall, NEXMD v2.0 expands the range of applications of NEXMD to a larger variety of multichromophore organic molecules and photophysical processes involving quantum coherences and persistent couplings between electronic excited states and nuclear velocity.

Semi-Empirical Shadow Molecular Dynamics: A PyTorch Implementation

Extended Lagrangian Born-Oppenheimer molecular dynamics (XL-BOMD) in its most recent shadow potential energy version has been implemented in the semiempirical PyTorch-based software PySeQM. The implementation includes finite electronic temperatures, canonical density matrix perturbation theory, and an adaptive Krylov subspace approximation for the integration of the electronic equations of motion within the XL-BOMB approach (KSA-XL-BOMD). The PyTorch implementation leverages the use of GPU and machine learning hardware accelerators for the simulations. The new XL-BOMD formulation allows studying more challenging chemical systems with charge instabilities and low electronic energy gaps. The current public release of PySeQM continues our development of modular architecture for large-scale simulations employing semi-empirical quantum-mechanical treatment. Applied to molecular dynamics, simulation of 840 carbon atoms, one integration time step executes in 4 s on a single Nvidia RTX A6000 GPU.

Extending machine learning beyond interatomic potentials for predicting molecular properties

Machine learning (ML) is becoming a method of choice for modelling complex chemical processes and materials. ML provides a surrogate model trained on a reference dataset that can be used to establish a relationship between a molecular structure and its chemical properties. This Review highlights developments in the use of ML to evaluate chemical properties such as partial atomic charges, dipole moments, spin and electron densities, and chemical bonding, as well as to obtain a reduced quantum-mechanical description. We overview several modern neural network architectures, their predictive capabilities, generality and transferability, and illustrate their applicability to various chemical properties. We emphasize that learned molecular representations resemble quantum-mechanical analogues, demonstrating the ability of the models to capture the underlying physics. We also discuss how ML models can describe non-local quantum effects. Finally, we conclude by compiling a list of available ML toolboxes, summarizing the unresolved challenges and presenting an outlook for future development. The observed trends demonstrate that this field is evolving towards physics-based models augmented by ML, which is accompanied by the development of new methods and the rapid growth of user-friendly ML frameworks for chemistry.

The Rise of Neural Networks for Materials and Chemical Dynamics

Machine learning (ML) is quickly becoming a premier tool for modeling chemical processes and materials. ML-based force fields, trained on large data sets of high-quality electron structure calculations, are particularly attractive due their unique combination of computational efficiency and physical accuracy. This Perspective summarizes some recent advances in the development of neural network-based interatomic potentials. Designing high-quality training data sets is crucial to overall model accuracy. One strategy is active learning, in which new data are automatically collected for atomic configurations that produce large ML uncertainties. Another strategy is to use the highest levels of quantum theory possible. Transfer learning allows training to a data set of mixed fidelity. A model initially trained to a large data set of density functional theory calculations can be significantly improved by retraining to a relatively small data set of expensive coupled cluster theory calculations. These advances are exemplified by applications to molecules and materials.

"Bottled" spiro-doubly aromatic trinuclear [Pd2Ru]+ complexes

Following an ongoing interest in the study of transition metal complexes with exotic bonding networks, we report herein the synthesis of a family of heterobimetallic triangular clusters involving Ru and Pd atoms. These are the first examples of trinuclear complexes combining these nuclei. Structural and bonding analyses revealed both analogies and unexpected differences for these [Pd₂Ru]⁺ complexes compared to their parent [Pd₃]⁺ peers. Noticeably, participation of the Ru atom in the π-aromaticity of the coordinated benzene ring makes the synthesized compound the second reported example of ‘bottled’ double aromaticity. This can also be referred to as spiroaromaticity due to the participation of Ru in two aromatic systems at a time. Moreover, the [Pd₂Ru]⁺ kernel exhibits unprecedented orbital overlap of Ru d_z² AO and two Pd d_xy or d_x²−y² AOs. The present findings reveal the possibility of synthesizing stable clusters with delocalized metal–metal bonding from the combination of non-adjacent elements of the periodic table which has not been reported previously.

Synthesis of a triangular [Pd₂Ru]⁺ complex with delocalized metal–metal bonding between non-adjacent elements of the periodic table, double aromaticity and overlap of d-AOs with different angular momentum.

Reply to the Comment on "Realization of Lewis Basic Sodium Anion in the NaBH3 - Cluster"

We reply to the comment by S. Pan and G. Frenking who challenged our interpretation of the Na^- :→BH₃ dative bond in the recently synthesized NaBH₃ ^- cluster. Our conclusion remains the same as that in our original paper (https://doi.org/10.1002/anie.201907089 and https://doi.org/10.1002/ange.201907089). This conclusion is additionally supported by the energetic pathways and NBO charges calculated at UCCSD and CASMP2(4,4) levels of theory. We also discussed the suitability of the Laplacian of electron density (QTAIM) and Adaptive Natural Density Partitioning (AdNDP) method for bond type assignment. It seems that AdNDP yields more sensible results. This discussion reveals that the complex realm of bonding is full of semantic inconsistencies, and we invite experimentalists and theoreticians to elaborate this topic and find solutions incorporating different views on the dative bond.

Can aromaticity be a kinetic trap? Example of mechanically interlocked aromatic [2-5]catenanes built from cyclo[18]carbon

Aromaticity serves as a kinetic trap for mechanically interlocked cyclo[18]carbon rings.

Correction: Can aromaticity be a kinetic trap? Example of mechanically interlocked aromatic [2-5]catenanes built from cyclo[18]carbon

Correction for ‘Can aromaticity be a kinetic trap? Example of mechanically interlocked aromatic [2-5]catenanes built from cyclo[18]carbon’ by Nikita Fedik et al., Chem. Commun., 2020, 56, 2711–2714.

Realization of Lewis Basic Sodium Anion in the NaBH3 - Cluster

We report a Na:^- →B dative bond in the NaBH₃ ^- cluster, which was designed on the principle of minimum-energy rupture, prepared by laser vaporization, and characterized by a synergy of anion photoelectron spectroscopy and electronic structure calculations. The global minimum of NaBH₃ ^- features a Na-B bond. Its preferred heterolytic dissociation conforms with the IUPAC definition of dative bond. The lone electron pair revealed on Na and the negative Laplacian of electron density at the bond critical point further confirm the dative nature of the Na-B bond. This study represents the first example of a Lewis adduct with an alkalide as the Lewis base.

Superoctahedral two-dimensional metallic boron with peculiar magnetic properties

A novel two-dimensional ferromagnetic stable boron material has been predicted and exhaustively studied with DFT methods. Its magnetism can be described by the presence of two unpaired delocalized bonding elements inside each distorted octahedron.

Aromatic character of [Au13]5+ and [MAu12]4+/6+ (M = Pd, Pt) cores in ligand protected gold nanoclusters – interplay between spherical and planar σ-aromatics

Ligand-protected superatoms are able to behave as both spherical and planar aromatic species, providing a strong link between spherical and planar σ-aromatics, which can be controlled selectively by tuning their redox charge states.

Insight into The Nature of Rim Bonds in Coronene

Coronene is known in chemistry as an aromatic or even superaromatic molecule while it has 24 π-electrons which does not conform to the 4 n + 2 Huckel's rule. Chemical bonding description of it is not settled in chemistry and five models were reported in the literature. According to our model, coronene has two concentric π-systems responsible for aromaticity inside of the molecule. In addition to that there are six peripheral 2c-2e π-bonds, which makes coronene aliphatic/aromatic at the same time. However, recent experiments and calculations put in question the presence of peripheral π-bonds. In order to resolve this issue, we computationally studied reaction mechanism of the Cl₂ molecule with C₂H₄, C₆H₆, and C₂₄H₁₂. As it turned out, coronene behaves in a way similar to ethylene by adding Cl₂ molecule. Thus, it proves that coronene indeed has peripheral double bonds which is also consistent with its experimental geometrical features. Our chemical bonding model allows to identify the most reactive atoms in coronene and other PAHs; therefore, it is a matter of importance for combustion and soot formation studies.